1. Field of the Invention
The present invention relates to methods and systems for optimization of a plurality of portfolios made up of tangible or intangible assets. More specifically, the present invention relates to methods and systems for optimization of multiple portfolios while applying portfolio constraints.
2. Discussion of the Background
Managers of assets, such as portfolios of stocks and/or other assets, often seek to maximize returns on an overall investment, such as, e.g., for a given level of risk as defined in terms of variance of return, either historically or as adjusted using known portfolio management techniques.
Following the seminal work of Harry Markowitz in 1952, mean-variance optimization has been a common tool for portfolio selection. A mean-variance efficient portfolio can be constructed through an optimizer with inputs from an appropriate risk model and an alpha model. Such a portfolio helps ensure higher possible expected returns (e.g., net of taxes and subject to various constraints) for a given level of risk.
Risk lies at the heart of modern portfolio theory. The standard deviation (e.g., variance) of an asset's rate of return is often used to measure the risk associated with holding the asset. However, there can be other suitable or more suitable measures of an asset's risk than its standard deviation of return. A common definition of risk is the dispersion or volatility of returns for a single asset or portfolio, usually measured by standard deviation. ITG Inc., the assignee of the present invention, has developed a set of risk models for portfolio managers and traders to measure, analyze and manage risk in a rapidly changing market. (See e.g., application Ser. No. 10/640,630). These models can be used to, among other things, create mean-variance efficient portfolios in combination with a portfolio optimizer, such as, e.g., those set forth herein.
According to modern portfolio theory, for any portfolio of assets (such as, e.g., stocks and/or other assets) there is an efficient frontier, which represents variously weighted combinations of the portfolio's assets that yield the maximum possible expected return at any given level of portfolio risk.
In addition, a ratio of return to volatility that can be useful in comparing two portfolios in terms of risk-adjusted return is the Sharpe Ratio. This ratio was developed by Nobel Laureate William Sharpe. Typically, a higher Sharpe Ratio value is preferred. A high Sharpe ratio implies that a portfolio or asset (e.g., stock) is achieving good returns for each unit of risk. The Sharpe Ratio can be used to compare different assets or different portfolios. Often, it has been calculated by first subtracting the risk free rate from the return of the portfolio, and then dividing by the standard deviation of the portfolio. The historical average return of an asset or portfolio can be extremely misleading, and should not be considered alone when selecting assets or comparing the performance of portfolios. The Sharpe Ratio allows one to factor in the potential impact of return volatility on expected return, and to objectively compare assets or portfolios that may vary widely in terms of returns.
By connecting a portfolio to a single risk factor, Sharpe simplified Markowitz's work. Sharpe developed a heretical notion of investment risk and reward—a sophisticated reasoning that has become known as the Capital Asset Pricing Model (CAPM). According to the CAPM, every investment carries two distinct risks. One is the risk of being in the market, which Sharpe called “systematic risk.” Systematic risk can be reduced by diversification. The other risk, “unsystematic risk,” is specific to a company's fortunes. These risks can also be mitigated through appropriate diversification. Sharpe discerned that a portfolio's expected return hinges solely on its “beta,” its relationship to the overall market. The CAPM helps measure portfolio risk and the return an investor can expect for taking that risk.
Portfolio optimization often involves the process of analyzing a portfolio and managing the assets within it. Typically, this is done to obtain the highest return given a particular level of risk. Portfolio optimization can be conducted on a regular, periodic basis, e.g., monthly, quarterly, semi-annually or annually. Likewise, one can rebalance portfolios, which is accomplished ultimately by changing the composition of the assets in a portfolio, as often as is desired or necessary. Since one is not required to rebalance a portfolio each time one optimizes, one can optimize as frequently as desired. In considering rebalancing decisions, one typically also considers tax and/or transaction cost implications of selling and buying as one pursues an optimal portfolio.
In some existing portfolio optimizers, techniques such as “hill climbing” or linear/quadratic programming are used to find optimal solutions. However, when using these techniques issues such as long/short, minimum position size, position count constraints, tax costs, and transaction costs generally cannot be modeled accurately. In addition, U.S. Pat. No. 6,003,018, titled Portfolio Optimization By Means Of Resampled Efficient Frontiers, shows other optimizer methods. The entire disclosure of U.S. Pat. No. 6,003,018 is incorporated herein by reference. The present invention provides substantial improvement over these and other optimizers.
The present assignee has developed a portfolio optimizer, the ITG Opt™ optimizer, which uses mixed integer programming (MIP) technology to produce more accurate results than previously used optimization and rebalancing systems. In a prior version, the ITG Opt™ system performed optimization in a single pass, taking into account simultaneously all of the constraints and parameters. In that version and security characteristic could be constrained or introduced. In addition, a full range of portfolio characteristics could have been specified, including, for example, constraints on leverage, turnover, and long vs. short positions. Furthermore, constraints may be applied to an entire portfolio or to its long or short sides individually. Furthermore, the prior version of ITG Opt™ avoided misleading heuristics by combining a branch-and-bound algorithm with objective scoring of potential solutions, thus reducing the size of the problem without damaging the integrity of the outcome.
Additionally, the prior ITG Opt™ optimizer could accurately model and analyze implications associated with the tax code. For example, integer modeling of tax brackets and tax lots enables the ITG Opt™ optimizer to minimize net tax liability without discarding large blocks of profitable shares. The prior ITG Opt™ is also adaptable to high in first out (HIFO), last in first out (LIFO), or first in first out (FIFO) accounting methods. In addition, the prior ITG Opt™ was designed with a focus on the real-world complexities of sophisticated investment strategies. The prior ITG Opt™ optimizer was able to handle complex and/or non-linear issues that could arise in real-world fund management.
Additionally, the prior ITG Opt™ optimizer was able to factor transaction costs resulting from market impact into its solutions. The optimizer included a cost model, ACE™, for forecasting market impact. The inclusion of ACE enabled users to weigh implicit transaction costs along with risks and expected returns of optimization scenarios.
Additionally, the prior ITG Opt™ optimizer used effective historical back-testing. The ITG Opt™ optimizer could closely track portfolios through time, accounting for the effects of splits, dividends, mergers, spin-offs, bankruptcies and name changes as they occur.
Additionally, the prior ITG Opt™ optimizer was equipped to handle many funds and many users. The prior ITG Opt™ optimizer included multi-user, client-server relational database management technology having the infrastructure to accommodate the demands of many simultaneous users and a large volume of transactions.
Additionally, the prior ITG Opt™ optimizer integrated neatly with trade-order management and accounting systems. Because the prior ITG Opt™ optimizer was built on relational database management technology it was easily linked with other databases. The prior ITG Opt™ optimizer could also generate trade lists for execution by proprietary TOM systems. Moreover, the prior ITG Opt optimizer design allowed for extensive customization of reports to fit a companies' operations and clients' needs. Moreover, custom report formats were able to be designed quickly and cost-effectively.
While a variety of portfolio optimization systems and methods, including prior versions of ITG Opt™ optimization system, may exist, there is a significant need in the art for systems and processes that improve upon the above and/or other systems and processes.